The rheology and microstructure of branched micelles under shear

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1 The rheology and microstructure of branched micelles under shear Michelle A. Calabrese, Simon A. Rogers, Ryan P. Murphy, and Norman J. Wagner Center for Neutron Science, Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware Synopsis The rheology and shear-induced structures of a series of self-assembled surfactant worm-like micelles (WLMs) with varying levels of branching are measured using rheo- and flow-small angle neutron scattering (SANS). The degree of branching in the mixed cationic/anionic surfactant (CTAT/SDBS) WLMs is controlled via the addition of the hydrotropic salt sodium tosylate and verified by cryo-tem. The linear viscoelasticity of the low salt (linear) micellar solutions is well-described as an extended Maxwell (Oldroyd-B) fluid, and samples exhibit shear banding under steady-shear flow. The linear viscoelasticity of more highly branched solutions deviates from Maxwellian behavior, where the plateau in G gradually increases in slope with increasing salt content. The higher salt solutions exhibit a shear thinning regime, followed by a shear thickening regime at high shear rates. Micelle segmental alignment in the flow-gradient plane is a nonmonotonic function of salt level and radial position. Spatially-resolved measurements of the segmental alignment corroborate shear banding in the linear WLMs, and the absence of shear banding with branching. Rheo-SANS measurements show that the onset of shear thickening at high rates corresponds to a structural transition. The results of this study link micellar microstructure and topology to the measured shear rheology of WLM solutions. I. INTRODUCTION Worm-like micelles (WLMs) are commonly used as a model system for studying polymers and polyelectrolytes [Magid (1998), Candau and Oda (2001)], and are of particular scientific interest due to their ability to selfassemble, break and reform under shear, and shear band [Spenley et al. (1993), Cates and Fielding (2006), Helgeson et al. (2009a)]. WLMs are ubiquitous in applications ranging from consumer products, cosmetics, and pharmaceuticals to industrial materials such as oil field fluids and drag reduction agents [Zakin et al. (1998), Yang (2002), Maitland (2000), Rogers et al. (2014)]. The tunable self-assembly of these living surfactant solutions enables a wide variety of solution morphologies and rheological characteristics that can be tailored for such applications. The linear rheology of WLMs is often well-described by an extended Maxwell (Oldroyd-B) model, where the structure breakage and reformation is significantly faster than reptation [Granek and Cates (1992), Cates and Candau (1990)] such that there is a single relaxation time. By altering the solution composition or temperature, a maximum in the zero-shear viscosity, η 0, is often observed, which has been shown to correspond to changes in the micellar topology. The increase in viscosity with added surfactant or salt results from micellar growth and entanglement. In contrast, micellar branching has been shown to lower η 0 [Candau and Oda (2001), Schubert et al. (2003), Ziserman et al. (2009), Sachsenheimer et al. (2014)], by providing another mechanism for stress relaxation. Unlike in polymers, micellar branch points are fluid and branches slide along a contour, thereby relieving stress. The presence of branches reduces the stress-carrying portion of the micelle to the sections between branch points. The effective micellar length is thus decreased by inducing branching, which leads to decreased viscosities [Candau and Oda (2001), Schubert et al. (2003), Lequeux (1992)]. As branching increases, large deviations from Maxwellian behavior are observed [Angelico 1 Corresponding Author: rogers.simon@gmail.com 1

2 et al. (2012), Palazzo (2013), Koshy et al. (2011)]. Further increases in salt concentration lead to network condensation [Liberatore et al. (2009), Thareja et al. (2011)]. In addition to serving as a model system that can aid future studies of branched polymers, branched WLMs are of particular scientific and industrial interest due to their tunable, highly non-newtonian flow properties. Linear WLMs tend to exhibit shear banding, a phenomenon where the flow exhibits spatial heterogeneities such that the material separates into regions of high velocity (low viscosity) and low velocity (high viscosity). Branched WLMs have shown the potential to eliminate the shear banding flow instability, which is suggested by the mitigation of the stress plateau along the flow curve [Rogers et al. (2014), Khatory et al. (1993), Berret et al. (1993), Lu et al. (2011)]. We note, however, that shear banding has been shown to be possible in models of entangled polymers that exhibit monotonic flow curves [Adams and Olmsted (2009)], such that the mechanism by which branching may or may not suppress shear banding is still under investigation. While shear thinning is optimal for injectable fracking and carrier fluids [Barati and Liang (2014)], shear banding is seemingly detrimental as fluid components may stratify or phase separate [Drye and Cates (1992), Schubert et al. (2004)]. While branching is widely accepted as an explanation of nonmonotonic zero-shear viscosity trends, there has been limited experimental evidence to corroborate this theory. Cryo-TEM is the most commonly used method, which provides visual evidence of branching [Ziserman et al. (2009), González and Kaler (2005), Kuperkar et al. (2008), Shrestha et al. (2011)]. However, this method is limited to dilute solutions and is difficult to use in studies of WLMs due to the elastic nature and high viscosities of the solutions. The blotting procedure performed while preparing cryo-tem grids may also enforce aligned structures, and the organic nature of the materials leads to poor image quality, making quantifying information from the images difficult. PGSE-NMR diffusion measurements have been successfully used to confirm the presence of branching in reverse micellar solutions of lecithin and oil [Angelico et al. (2012), Palazzo (2013)], with deviations from Maxwellian behavior observed at high frequencies. Koshy et al. (2011) noted differences in the scaling laws for Maxwell fluids [Granek and Cates (1992), Cates and Candau (1990)] past the viscosity maximum in solutions of catanionic CTAB-NaOL. As the observed scaling of the plateau modulus, G 0 N, was stronger at lower surfactant concentrations than at higher values where branching was proposed, it was concluded that G 0 N of branched systems has a weaker dependence on surfactant concentration than linear worm-like solutions. Oelschlaeger et al. (2008) used DWS optical microrheology and macroscopic mechanical rheology to investigate the underlying cause of two local maxima in the zero-shear viscosity and relaxation time in solutions of CPyCL with added NaSal. They determined that the peak at low salt concentration was a transition between linear micellar growth and micellar branching. Recently, Sachsenheimer et al. (2014) investigated six different WLM systems covering a broad range of surfactant concentrations and salt/surfactant ratios using capillary breakup elongational rheometry (CaBER). The filament lifetime, t fil, measured from the CaBER experiments was shown to depend on the plateau modulus, G 0 N, and the breakage time, τ break, obtained from small-amplitude oscillatory shear rheology parameters by the scaling law t fil /G 0 N τ 2/3 break. Furthermore, it was shown that the filament lifetime depends more strongly on the zero-shear viscosity in the case of linear micelles than in the branched regime, suggesting that CaBER can be used to distinguish micellar topology. Scattering techniques have also been developed for the determination of branching [Burchard (1999)]; however, it is generally accepted that static scattering can detect micellar growth but is insufficient to determine branching [Koshy et al. (2011), Kuperkar et al. (2008), Shrestha et al. (2011), Walker (2009)]. These, and related methods, are reviewed by Rogers et al. (2014). To investigate the effects of micellar branching on the steady-shear flow properties and possible shear banding instabilities, we propose a combination of nonlinear rheology and neutron scattering techniques (flow- SANS) with spatial and temporal resolution to determine the microstructural transitions that affect the macroscopic flow behavior [Eberle and Porcar (2012)]. Here, we explore the relationship between branching, microstructure, and nonlinear responses under steady shear flows using a model WLM system, where the phase behavior and microstructural length scales were systematically characterized by Schubert et al. (2003). The system is composed of mixed cationic and anionic surfactants cetyltrimethylammonium tosylate (CTAT) and sodium dodecyl benzene sulfonate (SDBS) near the overlap concentration (C C D =1.5% wt) and branching 2

3 is induced by the addition of the hydrotropic salt sodium tosylate (NaTos). In addition to flow-sans measurements in two of the three deformation planes, cryo-tem and shear rheological measurements are used to provide a comprehensive analysis of the effect of added salt on the structure and flow properties of WLMs. II. THEORY There are several methods of inducing branching in worm-like micellar solutions, generally via the addition of salt or oppositely charged ionic surfactants. Simple salts, such as NaCl, alter the ionic strength of solution but do not penetrate the structure of the micelles, thereby having less of an effect on the micelle topology as compared to the effect of hydrotropic salts such as NaSal or NaTos [Schubert et al. (2003)]. In this study, the total surfactant concentration C D is held constant at 1.5% wt (97/3% wt CTAT/SDBS) and NaTos is added from 0 to 0.25% wt solution total. Here, C D is approximately that of the overlap concentration, C, between the dilute and semi-dilute regimes, as determined by a change in the scaling laws at C D = 1.5% wt [Schubert et al. (2003)]. In the present WLM system, the use of oppositely charged surfactants is sufficient to induce branching at low levels with no added salt; thus the micellar growth region of increasing zero-shear viscosity is already surpassed. As the first viscosity maximum is not observed and the range of salt concentrations is sufficiently small so as to avoid phase separation, the zero-shear viscosity decreases monotonically with added salt. The overall micelle contour length, L c, is governed by the micelle scission energy, which is the difference between the endcap formation energy and the electrostatic energy of the micelle, E sciss = E c E e [MacKintosh et al. (1990)]. A low scission energy favors the formation of short, cylindrical micelles, whereas high scission energies lead to the formation of longer, worm-like micelles. In solutions with no added salt, the micellar head groups are primarily of the same charge, leading to stiff cylinders with a high electrostatic energy that repel each other. The addition of NaTos increases structural flexibility by screening headgroup repulsions and inter-micelle electrostatic interactions, thus reducing the net micelle surface charge. The reduction of the electrostatic energy of the system thereby increases the scission energy. The increasing scission energy makes the formation of branch points more energetically favorable [Schubert et al. (2003), MacKintosh et al. (1990)]. The penetration of the small molecule NaTos into the micelle also increases flexibility, enabling the surfactants to more easily rearrange into junctions needed to form branches as opposed to conventional convex endcaps. Granek and Cates (1992) and Cates and Candau (1990) describe the stress relaxation of linear worm-like micelles by a combination of reptation, breakage, and reformation dynamics. While strictly applicable to nonionic systems, the theory and scaling laws agree reasonably with experimentally-measured values when applied to the ionic, linear systems in this work. In the fast-breaking limit, the time required for a micelle to reptate out of its tube is much greater than the breakage time, so that any linear chain undergoes many breakage and recombination events before reptation processes alone could relax the entirety of the material stress. Linear worm-like micelles in the fast-breaking limit are therefore well described by a simple Maxwell model with a single relaxation time, τ R [Granek and Cates (1992), Cates and Candau (1990)]. The relaxation time for a Maxwell fluid is related to the breakage and reptation times (τ reptation, τ break ) via τ R = (τ break τ reptation ) 1/2 [Cates and Candau (1990)]. Small amplitude oscillatory shear measurements are often used to determine τ R, which in a Maxwell framework is defined as the timescale (inverse of the angular frequency) at which the dynamic moduli are equal. At the crossover frequency ω c, G (ω c ) = G (ω c ) and τ R = 1/ω c. A parametric representation of the linear viscoelastic (LVE) data, often referred to as a Cole-Cole plot, where G is plotted against G, is perfectly semicircular for a Maxwell fluid. In linear WLMs, the experimental data shows excellent agreement with the Maxwell model at low frequencies. However, as the angular frequency increases, deviations from the model, including a local minimum in G, are observed due to Rouse modes [Granek and Cates (1992)]. The frequency at which G exhibits a local minimum, ω min, gives an estimate of the breakage time (ω min 1/τ break ) and can be related back to the contour and entanglement lengths for linear, nonionic micelles (l e and L c, respectively) by G min /G l e /L c [Granek and Cates (1992), Granek (1994)]. From the theory of rubber elasticity, the entanglement length is related to the mesh size, ξ M, by l e ξ 5/3 M /l2/3 p [de Gennes (1979), Doi and Edwards (1986)]. The mesh size can then also be estimated by ξ m (k B T/G 0 N )1/3 [de Gennes (1979), Doi and Edwards 3

4 (1986)]. The extended Maxwell or Oldroyd-B model, where G is augmented with a high shear rate viscosity (G = G Maxwell + η ω), satisfactorily captures this high frequency behavior. Notably, the more charged or branched the system, the higher the expected deviation from such scaling laws. Lequeux (1992) extended the results of Cates to interconnected networks of micelles, in which branch points move fluidly along a contour and act as another mechanism for stress relaxation unlike in chemicallybonded polymers. As branch points form, the length scales defined for linear micelles, such as the entanglement length, become ill-defined. The effective micelle length becomes the distance between branch points, leading to a decreased zero-shear viscosity. Consequently, the sliding branch points decrease the reptation time, τ rep, and therefore the material relaxation time, τ R. In linear WLMs in the fast breaking limit, breakage and reformation dynamics lead to a single relaxation time, which is manifested as a semi-circle in the Cole-Cole representation. However, LVE data from polymeric systems, where breakage and reformation are not available mechanisms for stress relaxation, are almost never semicircular in the Cole-Cole representation. While both systems have inherent polydispersities in the average chain length, the chemically-bonded nature of the polymer requires reptation of the full chain for complete stress relaxation, whereas the living nature of the micelles leads to a single effective chain length. Polymeric branching also leads to significant deviations from Maxwellian behavior [Hatzikiriakos (2000)] and increases in viscosity because the branch points are not mobile as they are for WLMs. Similar trends have been observed in micellar solutions with high salt concentrations and branching [Khatory et al. (1993), Berret et al. (1993), Lu et al. (2011)], with anomalous behavior at high frequencies. Therefore, as branching increases and more mechanisms of relaxation become available, the LVE rheology increasingly deviates from Maxwellian behavior. III. MATERIALS AND METHODS A. Materials The WLM system presented was previously well-characterized over a range of added salt concentrations [Schubert et al. (2003)]. The WLM solutions are composed of mixed cationic and anionic surfactants CTAT and SDBS with a total surfactant concentration held constant at 1.5% wt (97/3 weight ratio of CTAT/SDBS; 35.8 mm CTAT/1.45 mm SDBS). Sodium tosylate (NaTos) was added as a hydrotropic salt to induce structural changes, ranging from 0.0% wt NaTos to 0.25% wt NaTos. Sodium tosylate and CTAT were obtained from Sigma-Aldrich. CTAT was recrystallized twice from a 50/50 mixture of ethanol and acetone. Sodium tosylate was used as received. Soft-type (linear chain) SDBS was obtained from TCI and used as received. All surfactant solutions were prepared at room temperature in D 2 O (Cambridge Isotopes, 99.8%) that was filtered before use. All samples were incubated in a 35 C water bath for 3 days before performing SANS or rheological measurements to ensure chemical, kinetic, and thermal stability. B. Cryo-TEM Cryo-TEM imaging was performed on a Technai G2 12 Twin TEM operating at 120 kv. Samples were prepared using an FEI Vitrobot at 35 C and 100% relative humidity. Prior to sample preparation, the TEM grids (Quantifoil R 2/1 or lacey carbon) were plasma cleaned for 60 s. A 3 µl volume of each sample solution was pipetted onto the grid inside the sample chamber. Using an automated system, each sample was blotted twice to remove excess sample prior to vitrification in liquid ethane. The blotting conditions were consistent for each sample: 3 s blot time, 5 s wait time, 10 s drain time, and 0 blot force. The grids were transferred into liquid nitrogen for storage before imaging. Images were recorded using a Gatan CCD camera and were imaged at a nominal underfocus to enhance phase contrast. The temperature of the probe was maintained between -178 and -180 C during imaging. 4

5 C. Rheometry The main rheology experiments were performed on a 0.01% wt NaTos solution (low salt) and a 0.10% wt NaTos solution (high salt) with supplementary experiments performed on other salt concentrations. All rheometry measurements were performed at 35 C ± 0.1 C. Reported rheological tests were performed on an ARES G2 strain-controlled rheometer (TA Instruments, New Castle, DE) with temperature control from a ThermoCube circulating chiller (AMS Technologies). A concentric-cylinder Couette geometry was used with a stationary inner cylinder, stainless steel DIN bob (R 1 = mm) and a rotating outer cylindrical cup (R 2 = mm), such that the gap width, H, was 1.16 mm. The position within the gap is notated as r/h. Using the length of the Couette bob, L, the resulting aspect ratio, Γ = L/H, was 35 and the gap to radius ratio, ε = H/R 1, was Select rheological measurements were repeated on an Anton-Paar MCR-501 stress-controlled rheometer operating in strain-controlled mode. Two separate concentric-cylinder Couette geometries were used, both with a moving inner cylinder and stationary outer cup and a solvent trap filled with D 2 O to provide a saturated atmosphere. In the first configuration R 1 = 24.0 mm and R 2 = 25.0 mm, resulting in ε = and Γ = 36. In the second configuration R 1 = 13.5 mm and R 2 = 14.5 mm, such that ε = and Γ = 36. Rheology was verified to be independent of instrument and geometry. Samples were conditioned in the rheometer for 10 minutes at 35 C to achieve thermal equilibrium. Frequency sweeps were then performed using a strain amplitude of 5% to measure the linear viscoelastic response of each sample. The delay time between measurements was at least 10 times that of the material relaxation time, determined by the crossover frequency (τ R = 1/ω c ). Initial sweeps were performed in triplicate over the course of one hour to ensure structural and thermal equilibrium after loading. Sweeps were performed over a frequency range of ω = 0.01 to 25 rad s 1 (increasing and decreasing) for the sample with low salt (0.01% wt NaTos) and from ω = 0.1 to 25 rad s 1 (increasing and decreasing) for the sample with high salt (0.10% wt NaTos). Hysteresis was not observed using this protocol. Amplitude sweeps were performed at the frequency limits to verify that the dynamic moduli are independent of strain amplitude at 5%. Corroborative frequency sweeps were performed at several strain amplitudes (5% to 20%) and using correlation and waveform analysis. Steady shear flow sweeps were performed on both samples to measure the steady-state material viscosity and stress over a range of shear rates ( s -1 ). Sweeps were performed in the increasing and decreasing directions with at least 10τ R of rest time between each datum without observable hysteresis. The flow curves were verified to be those of the steady-state with long-time ( s) stress and viscosity measurements from peak hold tests. To examine the stability of the flow near the shear thickening regime observed at high rates, additional startup measurements were performed in both the ARES and MCR rheometers for s on the high salt sample (0.10% wt NaTos). In both geometries, the stress fluctuations were 3.5% or less at steady state (t > 10 s). These results are detailed further in the Supporting Information. Frequency sweeps were also performed after each rheological test to confirm the absence of foaming, evaporation, or irreversible changes from shear. D. Static SANS measurements Static SANS measurements were taken at the National Institute of Standards and Technology (NIST) Center for Neutron Research in Gaithersburg, MD on the NG-7 30 m SANS instrument [Porcar et al. (2011)]. Samples were measured in 2 mm quartz cells with temperature control set to 35 C ± 0.1 C to prevent crystallization of the material. The measured scattering vector, q, ranged from Å -1 to 0.5 Å -1 using detector distances of 15.3 m (lens), 4 m and 1 m. The neutron wavelength, λ, was 6 Å for the 4 m and 1 m configurations, and 8.4 Å for the 15.3m with lens configuration. The wavelength spread, λ/λ, was 11.5% for both wavelengths. Raw data was reduced to an absolute scale as outlined by NIST standards by accounting for background, empty cell scattering, and detector efficiency [Kline (2006)]. Absolute scattering profiles were shown to be independent of instrument and sample environment from additional static SANS experiments at NIST and on the D-22 instrument at the Institut Laue-Langevin (ILL) in Grenoble, France. Measurements from six additional configurations showed excellent agreement (see Supporting Information): NG-7 with Anton-Paar MCR501 5

6 rheometer, NG-7 with 1-2 shear cell, NG-3 30 m SANS with 2 mm quartz cells, NG-3 with rheometer, NGB- 30 with rheometer, NGB-10 with rheometer, and D-22 (ILL) with 1-2 shear cell. E. Rheo-SANS measurements in the 1-3 (flow-vorticity) plane Rheo-SANS experiments in the 1-3 (flow-vorticity) plane were conducted at the NIST Center for Neutron Research on the NGB 30m SANS instrument. An Anton-Paar MCR-501 stress-controlled rheometer (used in strain-controlled mode) with a concentric-cylinder Couette geometry was used for all experiments. The rheometrical geometry was composed of a titanium moving inner cylinder and stationary outer cup as previously stated (R 1 = 24.0 mm; R 2 = 25.0 mm; Γ = 36; ε = 0.042). A solvent trap filled with D 2 O was utilized to provide a saturated atmosphere and to limit sample evaporation. The neutron wavelength, λ, was 6 Å with a wavelength spread λ/λ = 13.1%. Two detector distances (8 m, 1.65 m) were used to cover a q-vector ranging from Å -1 to 0.2 Å -1. Results were corroborated with select rheo-sans experiments on the NG-3 instrument using a Couette geometry with a 0.5 mm gap (R 1 = 13.5 mm; R 2 = 14.0 mm; Γ = 36; ε = 0.042) and on the NGB-10 instrument using a Couette geometry with a 1.0 mm gap (R 1 = 13.5 mm; R 2 = 14.5 mm; Γ = 36; ε = 0.042). Two vertically-oriented beam apertures were placed prior to the rheometer to minimize spatial smearing that results from the rheometer curvature. The apertures limit the scattering volume to a small region where the flow direction, beam direction, and slit orientation are mutually orthogonal, with the beam and flow directions spanning the horizontal plane. A 5 mm x 20 mm source aperture was positioned at the end of the neutron guides. A sample aperture (2 mm x 20 mm slit) was centered approximately 3 inches prior to the quartz windows of the rheometer. Select experiments were repeated with a 3 mm x 20 mm source aperture and no significant resolution effects were observed. F. Flow-SANS measurements in the 1-2 (flow-gradient) plane Flow-SANS experiments in the 1-2 (flow-gradient) plane of shear were conducted at both the NIST Center for Neutron Research and the Institut Laue-Langevin. All experiments were performed in a short gap Couette cell (5mm path length) as previously described [Liberatore et al. (2006), Gurnon et al. (2014)]. The shear cell consists of a rotating inner cylinder (R 1 = 25.5 mm) and an outer stationary cylinder (R 2 = 26.5 mm) such that the gap width is 1.0 mm, Γ = 5 and ε = Temperature control is maintained by using a flow-through port within the cell that is connected to a heated water bath (35 C ± 0.1 C for all experiments). Two cadmium beam slits are placed prior to the front wall of the shear cell. The first is a 5 mm slit oriented horizontally which constrains the measured region to one where the flow is essentially vertical. The second slit is oriented vertically, and has a width based on desired spatial resolution. A stepper motor is used to translate the slit across the gap, providing spatial resolution. The motor is calibrated by taking empty cell transmission measurements across the cell gap. The edges of the gap are identified by the large changes in the number of transmitted neutrons from the aluminum to the fluid (air) in the empty cell [Liberatore et al. (2006), Gurnon et al. (2014)]. Steady-shear experiments were performed over a range of shear rates. Empty cell and sample transmission measurements were taken at each spatial position across the gap. Samples were allowed to equilibrate for a minimum of 30 minutes after loading, and multiple static measurements were taken during the equilibration period to identify any structural changes. Any bubbles were removed from the cell before the start of each experiment. Static structure measurements were taken at the end of every five steady-shear experiments to ensure that the sample had not been subjected to bubbling, evaporation, or irreversible changes from shear. Data was reduced to an absolute scale as outlined by NIST standards [Kline (2006)]. The primary flow-sans experiments were performed at NIST using the NG-7 30m SANS instrument. All NIST experiments were performed with a 0.1 x 3 mm straight secondary beam slit. Measurements were taken at several positions across the gap, ranging from r/h = 0.1 to r/h = 0.9. The main experiments were performed using an aluminum shear cell with magnetic coupling, with one aluminum window and one quartz window to view the sample. Steady-shear scattering experiments were performed with a detector distance of 8 m and 6 Å neutrons for a minimum of one hour. The measured scattering vector, q, ranged from Å -1 to 0.05 Å -1 6

7 with λ/λ = 11.5%. Complimentary steady-shear experiments were conducted in a titanium shear cell for a minimum duration of one hour at a detector distance of 8 m with 6 Å neutrons and a wavelength spread of λ/λ = 11.5%. The q-range in those experiment covered the range Å -1 to 0.05 Å -1. Select experiments on the sample with low salt (0.01% wt NaTos) were performed on the D-22 SANS instrument at ILL. Experiments were performed at a detector distance of 11.2 m with 6 Å neutrons and a wavelength spread of λ/λ = 10%. A 0.3 mm wide curved slit was used for these experiments. Experiments were performed at two positions located near the inner (r/h = 0.3) and outer wall (r/h = 0.7) of the shear cell. Steady-shear experiments were conducted for 10 minutes covering a q-range of Å -1 to Å -1. Repeated experiments at a detector distance of 17.6 m yielded identical results within error, indicating that the decrease in resolution from 17.6 m to 11.2 m was insignificant. IV. RESULTS Results are presented from micellar solutions with different salt content, ranging from 0.0% wt NaTos to 0.25% wt NaTos. In order to remove micellar growth and shape as confounding variables when determining the effects of added salt, all samples studied are at surfactant and salt concentrations past the commonly observed viscosity maximum. Here, the micelles are truly worm-like, where the persistence and contour lengths are well-separated (l p << L c ), thus removing effects that may be attributed to the shape and length of shorter, rodlike micelles. To verify the expected structure of the micelles, cryo-tem, static SANS, and linear viscoelastic (LVE) regime rheology measurements were performed. These structural results and the linear viscoelastic rheology were favorably compared with the results of Schubert et al. (2003). Following the structure confirmation and LVE rheology, the effect of added salt on the rheology and flow-induced structure of the micelles was examined. These results are restricted to a direct comparison of two samples from two salt regimes of interest: 0.01% wt NaTos (referred to as low salt) and 0.10% wt NaTos (high salt). A. Structure Confirmation 1. Cryo-TEM Cryo-TEM was performed on solutions with a fixed surfactant concentration (C D = 1.5% wt) and various salt concentrations to visualize the effect of salt concentration on the structure: low (0.01% wt NaTos), high (0.10% wt NaTos), and very high salt (0.15% wt NaTos). Here, the surfactant concentration lies on the boundary of the dilute and semi-dilute regimes (C D = C 1.5% wt), as noted by a change in the micellar scaling laws at this concentration [Schubert et al. (2003)]. As opposed to inducing structural changes such as branching by changing the surfactant concentration, the structure of these solutions is controlled by a change in the concentration of added salt. A qualitative distinction between the resulting structures is observed in Figure 1, where the 0.01% wt NaTos (a, red) and 0.10% wt NaTos (b, blue) worm-like micelles are compared. Additional images of these two solutions, along with images of the 0.15% wt NaTos solution, can be seen in the Supporting Information. Figure 1a (red) shows the 0.01% wt NaTos solution containing linear micelles and no observable branch points. In contrast, the 0.10% wt NaTos solution shown in Figure 1b (blue) shows a high probability of finding a branch point along a contour, and contains a variety of loops and branch points. While the concentration makes it difficult to differentiate between branch points and overlapping micelles, the white arrows point to clear loops or three-fold junctions where overlap does not occur. These junctions and other irregular structures are also observed in the very high salt (0.15% wt NaTos) solution (Supporting Information), and become more prevalent with the addition of the hydrotropic salt. The structures are consistently observed across multiple images from different grid locations. These results are consistent with the findings of Schubert et al. (2003), where branching was proposed with increasing hydrotropic salt content. While all samples undergo the same preparation and imaging conditions, flow-aligned structures are observed in the linear system (0.01% wt NaTos) that are absent in the samples of higher salt content. This alignment is difficult to avoid and is enforced by the 7

8 micellar topologies: the linear structures align more easily than those containing branch points or network-like structures that introduce steric effects. The insets show the larger-scale structural differences, where long thread-like micelles (a) and interconnected structures (b) are observed. The micellar diameter, d cs, was estimated to be between 40 Å and 50 Å for all samples using ImageJ analysis on multiple images. Micellar diameter was not a function of salt concentration within the precision obtainable by cryo-tem. The diameter measurements agreed with the cross-sectional radius of 21.4 Å (d cs = 42.8 Å) determined by Schubert et al. (2003) via static SANS. Additionally, Schubert et al. (2003) calculated the contour length of the micelles to be on the order of several microns, which was supported with additional cryo-tem images. Qualitatively, the number of branch points is much higher in the 0.10% wt NaTos sample (and 0.15% wt NaTos sample) than in the 0.01% wt NaTos sample. Although these and additional images in the Supporting Information show the formation of branch points with added NaTos, due to the limited contrast and the tendency of the samples to shear align with the cryo-tem grid, no quantitative relationships between NaTos content and structure have been developed. Figure 1: Comparison between CTAT/SDBS worm-like micellar solutions with a fixed surfactant concentration (C C D =1.5% wt) with low salt (a, 0.01% wt NaTos, red) and high salt (b, 0.10% wt NaTos, blue). (a) Chains are highly linear. The inset provides a larger scale view of the long, linear structures apparent throughout the sample. (b) Micelles have identifiable branch points and form a variety of junctions, loops, and other structures. The inset shows the larger scale morphology that contrasts the linear micelles observed in the (a) inset. 2. SANS Static small angle neutron scattering measurements were performed to determine the equilibrium structures and micellar length scales of the WLMs with varying salt content [Schubert et al. (2003)]. SANS results were used to calculate the micellar radius using several models, which was then quantitatively compared to the cryo-tem estimates and the length scales determined by Schubert et al. (2003). Figure 2 shows the 1-D azimuthally-averaged SANS measurements in the full q-range from Å -1 to 0.5 Å -1 corresponding to real space dimensions on the order of 10 Å to 6000 Å. A 2-D isotropic scattering pattern for the low salt system (0.01% NaTos, red) and high salt system (0.10% NaTos, blue) are shown to highlight the differences in the scattering between the two samples. In the low salt system, there is a strong interaction peak that appears in 8

9 the 2-D pattern as an intensity ring at q = Å -1. In real space, this q-value corresponds to a distance on the order of 300 Å, which is indicative of the preferred inter-micellar separation distance arising from the electrostatic repulsions between micellar segments. As the intensity is isotropic, the sample is also isotropic with no net alignment of the micellar segments. With increasing salt concentration, the electrostatic interactions are progressively screened and the interaction peak is dampened. In the 2-D scattering of the 0.10% wt NaTos system, the mitigation of the interaction peak is evident, as the ring structure is no longer visible. Figure 2: 1-D azimuthally-averaged static SANS for CTAT/SDBS WLM solutions with a range of salt (0.01% wt NaTos) to (0.25% wt NaTos). 2-D scattering patterns are highlighted for the low salt (0.01% wt NaTos, red) and high salt system (0.10% wt NaTos, blue). The strong interaction peak at low salt concentration manifests itself as a ring in the 2-D scattering pattern (red), whereas the electrostatic interactions are screened at high salt concentrations (blue), leading to the disappearance of the interaction peak. The 0.15% wt NaTos 1-D scattering is also shown (purple) to highlight the structural similarities between the 0.15% wt and 0.10% wt sample, in qualitative agreement with the cryo-tem results. The 1-D scattering of the 0.15% wt NaTos solution is also highlighted (purple + symbol) to show the structural similarities between this sample and the 0.10% wt NaTos solution. The similarity in the SANS between these two samples is supported by the cryo-tem results which show comparable features (see Supporting Information). At the maximum salt concentration shown in Figure 2 (C s = 0.25% wt), the interaction peak has completely disappeared. The high-q scattering (q 0.04 Å -1 ) for all samples collapses onto one curve, indicating that the basic cylindrical structure of the micelles does not change with salt concentration. To determine micellar length scales, scattering models for a cylinder and flexible cylinder were fit to the data in the high-q region beyond the influence of the interaction peak. As expected, both models yielded similar results and all cross-sectional radii, r cs, ranged from 20.2 Å to 21.3 Å. Using a simpler Guinier approximation yields r cs = 21.2 Å to 21.9 Å, in good agreement with the Guinier analysis of Schubert et al. (2003) where r cs = 21.2 Å to 21.6 Å. As expected, the cross-sectional radius of the micelles slightly decreases with increasing salt concentration, due to screened repulsions that decrease the effective headgroup size. 9

10 B. The effect of hydrotropic salt on the rheology of WLMs 1. Relaxation time and zero-shear viscosity as a function of added salt The material relaxation time, τ R, and the zero-shear viscosity, η 0, of the WLMs over the range of added salt (0.0% wt % wt NaTos) were examined as a function of salt concentration and the ratio of the concentrations of the ions, which self-assemble to form the micelles. SDBS and NaTos dissociate to form negatively charged ions and CTAT forms positively charged ions in solution. The material relaxation time is defined as τ R = 1/ω c, where ω c is the angular frequency at which G and G are equal in the linear viscoelastic regime (crossover frequency). The zero-shear viscosity and an estimate of the shear relaxation time, τ v, were determined by fitting the Cross Model (Equation 1) [Cross (1965)]: η( γ) = η + η 0 η 1+( γτ v) m (1) where η is the high shear viscosity and the exponent m = N + 1 and ranges between 1.0 and 1.7, where N is the power law index. Figure 3: Zero-shear viscosity, η 0, and rheological relaxation time, τ R, as a function of salt concentration (a) and ion concentration ratio (b). Both parameters are decreasing functions of salt and ion ratio, indicating that the system has surpassed the commonly-observed first viscosity maximum in WLM systems. The range of salt concentration is limited such that a second viscosity maximum is not observed. The associated error in both metrics determined in samples with multiple preparations is smaller than the symbol size. For the surfactant concentration used here (C D = 1.5% wt CTAT/SDBS in 97/3 wt ratio), Schubert et al. (2003) indicated that η 0 and τ R of the micelles decrease monotonically as a function of increasing salt concentration over the range of C s = 0 to 0.25% wt NaTos. Figure 3a confirms this trend in both η 0 and τ R. At C D = 1.5% wt, the micelles are very long, even at low salt concentrations, as evidenced by the cryo-tem images. Accordingly, the commonly-observed viscosity maximum is effectively shifted to negative salt concentrations at this concentration of mixed surfactant. The viscosity maximum is only observed at lower surfactant concentrations with increasing salt concentration at the 97/3 weight ratio of CTAT/SDBS [Schubert et al. (2003), Koehler et al. (2000)]. The decreases in η 0 and τ R with increasing ion concentration ratio scale with similar dependences, and are comparable to the viscosity and relaxation time trends reported by Sachsenheimer et al. 10

11 (2014) for related WLM solutions, including CTAB/NaSal (Figure 3b). The observed trends are qualitatively similar to those of the CTAB/NaSal solutions between the two observed viscosity maxima (as a function of ion concentration), which is expected given the functional and structural similarities between both surfactants and salts [Sachsenheimer et al. (2014)]. In the present study, a second viscosity maximum was not observed, which is likely due to the limited range of salt concentrations examined. 2. Linear viscoelastic (LVE) regime rheology as a function of added salt The linear viscoelastic rheology of the samples (0.01% % wt NaTos) was measured to determine characteristic differences with added salt and to estimate characteristic length and time scales. Results were compared to an extended Maxwell (Oldroyd-B) model as previously performed [Liberatore et al. (2009), Helgeson et al. (2009b)]. As seen in Figure 4a, the crossover frequency, ω c, increases with increasing salt content. As τ R is the inverse of the crossover frequency, τ R of the high salt (0.10% wt NaTos) sample is an order of magnitude shorter than that of the low salt case (0.01% wt NaTos). The LVE rheology shows that the value of the moduli at the crossover point (G c (ω c )) is not significantly affected by low levels of salt. However, G c increases significantly at high salt content, as observed in the 0.185% and 0.25% wt NaTos samples. Figure 4: Dynamic moduli across the range of salt concentrations studied (0.01% wt NaTos to 0.25% wt NaTos). (a) The low salt system is a nearly perfect extended Maxwell fluid over the range of angular frequencies investigated with the exception of a slight upturn in G in the plateau region. With increasing salt content, the upturn in G at ω > ω c becomes increasingly significant, and the 0.25% wt NaTos sample has no apparent plateau over the frequency range. (b) Deviations from the extended Maxwell model with increasing salt concentration are more apparent when the moduli are normalized by the crossover modulus, G c and compared vs. De. The low frequency LVE for the WLMs is dominated by changes in the relaxation time due to the addition of hydrotropic salt but is otherwise qualitatively similar. As salt concentration increases, the Deborah number (De = ωτ R ) at which deviations from Maxwellian behavior occur decreases, as seen in Figure 4b, where the dynamic moduli are normalized by G c and the frequency by ω c. For example, the Deborah number of the G minimum at high frequency decreases systematically with added salt. The slope of the plateau in G gradually increases with added salt until the G plateau essentially disappears when C s 0.185% wt NaTos. These deviations in LVE behavior are in agreement with results from Khatory et al. (1993), where the deviations from Maxwellian behavior in the Cole-Cole representation of the data increase significantly as the salt concentration, and therefore correlation length, increases. 11

12 3. Steady shear rheology of 0.01% and 0.10% wt NaTos solutions In order to compare the specific effects of added salt on the shear rheology, the steady-state viscosity and stress were compared both at equivalent shear rates (Figure 5a) and Weissenberg numbers (Figure 5b) for the 0.01% wt NaTos (low salt) and 0.10% wt NaTos (high salt) samples. Here, the Weissenberg number, W i, is the product of the shear rate and the material relaxation time, W i = τ R γ. Figure 5 shows shear thinning behavior in both samples, where the zero-shear viscosity, like the relaxation time, decreases by an order of magnitude with an order of magnitude increase in added salt content. Results were fit by the Cross Model (Equation 1) to yield η 0,low salt = 34 Pa s and η 0,high salt = 2.6 Pa s (Table 1). Figure 5: Steady-shear flow curve of the low (0.01% wt NaTos) and high salt (0.10% wt NaTos) solutions on an absolute scale (a) and Weissenberg number scale (b). Figure 5 shows that while the difference in stress between the two samples is a nonmonotonic function of shear rate, the stress is always higher in the high salt case at an equivalent W i. Ultimately, this trend in the stress is a result of the shear thinning response and how it differs in the two solutions. Whereas both samples shear thin, the degree of shear thinning is mitigated by adding salt, which can be observed by the slope in the viscosity curves of k = -1 in the low salt system (red) and k = in the high salt system (blue). This translates to a power law index of N = 0 in the low salt sample and N = 0.15 in the high salt sample. The power law index N = 0 applies to the stress plateau in the low salt sample (red), which spans a wide range of shear rates (W i = 1 to W i 300). The stress plateau is strongly suggestive of shear banding at these shear rates. Beyond the shear banding region, the viscosity in the low salt sample begins to approach its minimum, high rate value, η. In the high salt sample (blue), the stress maintains a positive slope, which covers a much smaller range of shear rates (1 W i 40) and is indicative of a strongly shear thinning solution. At high shear rates and Weissenberg numbers, the high salt system shows reproducible shear thickening behavior. The shear thickening is highly repeatable amongst additional sample preparations and is also observed in samples with higher salt concentrations. Upon shear startup, it is well known that shear banding can take hundreds of seconds to develop in a worm-like micellar solution [Grand et al. (1997), Britton and Callaghan (1999), López- Barrón et al. (2014)]. In the low salt sample, the steady-state stress response is observed only after s, at minimum, for the shear rates in the stress plateau, which is consistent with shear band formation. Conversely, the steady-state stress response in the high salt solution is achieved rapidly after shear startup (< 10s) for all shear rates shown, in accordance with shear thinning. Table 1 provides a summary of the differences in the length and time scales between the two samples, determined from rheology and SANS data. Also included are estimates of length scales that can be derived 12

13 Table 1: Characteristic length and time scales of low and high salt (0.01%, 0.10% wt NaTos) WLMs Time or length scale Method Low salt High salt ω c (rad s 1 ) LVE rheology τ R (s) LVE rheology η 0 (Pa s) Steady shear rheology η (Pa s) Extended Maxwell model N/A η (Pa s) Steady shear rheology N/A Power law index, N Steady shear rheology G 0 N (Pa) LVE rheology G min (Pa) LVE rheology τ break (s) LVE rheology/scaling laws τ rep (s) LVE rheology/scaling laws r cs (Å) cryo-tem r cs (Å) SANS flexible cylinder model r cs (Å) SANS, Schubert et al. (2003) 21.4 ± 0.2 ξ M (Å) scaling laws ξ M (Å) Schubert et al. (2003) (in H 2 O) l e /L c scaling laws l e (Å) scaling laws l e (Å) Schubert et al. (2003) N/A 2050 (in H 2 O) L c (Å) scaling laws 8,100 13,000 L c (Å) Schubert et al. (2003) N/A 21,000 (in H 2 O) l p (Å) SANS cylinder model l p (Å) rheo-optics, Schubert et al. (2003) 850 (0.05% NaTos) 310 (in H 2 O) from fits to SANS data or by micellar scaling laws [Granek and Cates (1992), Cates and Candau (1990), Granek (1994), de Gennes (1979), Doi and Edwards (1986)]. These length scales include the persistence length l p, mesh size ξ M, entanglement length l e, and contour length L c. While these scaling laws are most applicable to nonionic, linear micelles, the values are on the same order of magnitude as results from light scattering and other methods employed by Schubert et al. (2003), which are shown for comparison. It is to be noted that the majority of their measurements were performed in samples in water (as opposed to D 2 O) as the solvent, which can result in rheological differences [Lopez-Barron and Wagner (2011)]. Interpretation of these length scales for the high salt sample is to be cautioned as the theories do not explicitly account for topological changes that may result from adding salt. While it is difficult to derive quantitative information from cryo-tem, these predictions appear to be in line with observations from the images. C. The effect of hydrotropic salt on the shear-induced microstructure of WLMs plane rheo-sans As the rheological results suggest different mechanisms of shear thinning between the low (0.01% wt NaTos) and high (0.10% wt NaTos) salt samples, structural SANS measurements were performed to compare the flowinduced structures of the micelles at equivalent absolute shear rates. Rheo-SANS measurements were taken in the 1-3 (flow-vorticity) plane at nominal shear rates along the steady shear flow curves (Figure 6). Under shear flow, micellar segments often align in the flow direction [Rogers et al. (2014), Eberle and Porcar (2012), López-Barrón et al. (2014)]. These microstructural rearrangements can be quantified by a scalar alignment 13

14 factor [Walker and Wagner (1996)], calculated from the 2-D SANS patterns in a particular plane. The resulting anisotropy is quantified by the observed degree of increased intensity, in the q -1 (rod-like segment) scattering regime: A f = 2π 0 I(q,φ) cos(2(φ φ 0)) dφ 2π 0 I(q,φ) dφ (2) where I(q) is the intensity over a small fixed q-range and φ is the azimuthal angle and φ 0 is the azimuthal angle of maximum intensity. Note that in the case of 1-3 plane rheo-sans, φ 0 = 0 due to the symmetry imposed by the method. The intensity distribution, I(q), is a projection of the material orientation distribution function (ODF) onto a particular scattering plane [Burger et al. (2010)]. The benefit of using the alignment factor as opposed to another orientation parameter is that the underlying material intensity distribution can be directly used to calculate the microstructural rearrangements and subsequent degree of anisotropy. Often calculations of the Hermans orientation parameter require the intensity distribution, or orientation distribution function, to be assumed or fit to a particular model before the parameter can be derived and calculated [Burger et al. (2010)]. In micelles with varying topologies, a single orientation distribution, such as the commonly used Maier-Saupe potential for nematic liquid crystals [Walker and Wagner (1996), Maier and Saupe (1958, 1959)], may not be adequate to describe all systems. Figure 6 shows the scattering and alignment as a function of shear rate for the 0.01% and 0.10% wt NaTos samples. The aligned 2-D scattering patterns vary significantly between the two samples due to the presence of the interaction peak in the 0.01% wt NaTos sample. Figure 6 specifically emphasizes the 1-3 plane alignment factor and stress at shear rates within the flow curves where the samples exhibit a high degree of shear thinning. Despite differences in the steady-shear rheology between the samples, the alignment factors follow the same trend with increasing shear rate. The high salt sample has consistently lower values of the alignment factor until the viscosity upturn (shear thickening) is encountered. This trend is also observed in samples with higher salt content [Rogers et al. (2014)], where the alignment factor is lower at the same absolute shear rate than that of the low salt WLMs, until a critical shear rate is reached where the alignment factor for all WLM solutions collapses onto the same curve. Here, the alignment is independent of viscosity, stress, shear rate, and sample. To explore the shear thickening behavior of the high salt solution further, two points of roughly equal alignment between the two solutions are highlighted in Figure 6. The first set of points examined correspond to shear rates in the shear banding or shear thinning regime, while the second set correspond to rates greater than that of the observed shear thickening response. In the first pair of alignment factors, where A f 0.3, the nominal shear rates for equal alignment differ, as γ low salt = 45 s -1 and γ high salt = 90 s -1. As shear thickening occurs, the alignment factors approach the same value with increasing shear rate (A f 0.55), as shown by the the second pair of alignment factors ( γ low salt = γ high salt = 420 s -1 ). Figure 7 shows the orientation distribution function and the 1-D scattering of the low and high salt samples at these two points of equal alignment. The intensity distributions are normalized to provide a fair comparison of the samples. Sector-averaged scattering was performed in the anisotropy (vorticity) direction to determine the structure of the material aligning in the flow direction, which is common practice when analyzing anisotropic or flow-aligned scattering data [Helgeson et al. (2009b), Weigandt et al. (2011)]. In highly aligned samples, there is little to no scattering along the flow axis above background so the sector-average method focuses only on the aligned material. Because the intensity distribution is a projection of the overall material orientation, any changes to the intensity distribution result from changes to the ODF and the underlying material structure. Figure 7a shows the intensity distribution of the low and high salt samples at γ = 45 s -1 and γ = 90 s -1, respectively (A f 0.3). Despite having the same alignment factor values, the intensity distribution of the low salt sample is much sharper than that of the high salt sample, reflecting different underlying orientation distribution functions. The sector-averaged scattering in the vorticity direction (Figure 7b) for both the low and 14

15 high salt sample yields nearly identical scattering to its static structure. The change in the absolute intensity between the static and shear-induced structures results from the sector average method, where a larger fraction of the material is in the flow direction under shear as compared to the sample at rest, leading to a higher absolute intensity. Figure 6: Alignment factor and 1-3 plane rheo-sans scattering patterns of the low (0.01% wt NaTos) and high salt (0.10% wt NaTos) solutions at multiple shear rates across the steady shear flow curve. The mechanism of anisotropy clearly differs between the two series of scattering patterns due to the presence of the interaction peak in the low salt sample (red) and its absence in the high salt sample (blue). Resulting alignment factors are lower in the high salt case until the viscosity upturn. Two points of equal alignment between the systems are highlighted to be discussed further: one before and one after the viscosity upturn in the high salt solution. Between Figure 7a and c, clear differences in the intensity distribution and the 1-D sector-averaged scattering are observed in the high salt sample after the onset of shear thickening. When γ = 420 s -1, both samples have the same alignment factor (A f 0.55) and nearly identical normalized intensity distributions. The shape of the intensity distribution with angle remains the same for the low salt case, and is the same at all shear rates for this sample, resulting from a similar underlying ODF and material structure. Conversely, the intensity dis- 15

16 tribution for the high salt sample greatly sharpens from its original form, indicative of a change in structure. At shear rates higher than the shear thickening onset, a similar ODF is observed in the high salt sample as in the low salt sample (Figure 7c). A change in structure is also detected in the 1-D sector-averaged SANS (Figure 7d), where the peak at q = Å -1 that is not present in the high salt sample under static conditions now appears at high shear rates. In the direction of anisotropy, the structure of the high salt sample is now similar to the static structure of the low salt sample, and is quite dissimilar to its own static structure. Interestingly, the first shear rate at which this peak appears in the scattering is at the onset of shear thickening ( γ = 185 s -1 ); thus the rheological shear thickening can be linked to a change in the SANS structure of the high salt sample. Note that there are no permanent changes to the material structure, which reverts to its static form upon the cessation of shear. Figure 7: Normalized intensity distribution (a,c) and sector-averaged 1-D SANS in the anisotropy direction (b,d) for the low and high salt samples before (a,b) and after shear thickening (c,d), corresponding to the bolded points from Figure 6. (a) For the same alignment factor, the intensity distribution of the low salt sample is much sharper than the high salt sample, reflecting the micellar orientation and topology. (B) The SANS structure for the high salt sample under shear is nearly identical to the static high salt structure (blue line). (c) Both samples have the same alignment factor and nearly identical intensity distributions. This structural change is detected in the 1-D SANS (d), where the sector average scattering from the high salt system under strong flow is nearly identical to that of the low salt system (red line). In contrast, the structure for the low salt system under shear shows increased flow alignment but the correlation peak maintains its position with increasing rate. 16

17 We note that the 1-3 alignment factor can only provide SANS information that is convolved in space (across the Couette gap) as a function of the shear rate. When the alignment factor for the low salt sample is compared to the stress within the stress plateau, it is observed that the alignment factor increases steadily as the shear rate increases, despite the nearly constant stress. This likely corresponds with an increasing alignment and proportion of material within the high shear rate band with increasing shear rate. However, as the trends between the two systems are fairly similar, to truly resolve the nature of the material structure and flow properties across the gap, 1-2 plane structural measurements are necessary to gain spatial resolution plane flow-sans Spatially-resolved, 1-2 plane flow-sans measurements were performed at identical shear rates in order to distinguish spatially-dependent flow properties including shear banding. Measurements were taken at applied shear rates of 15, 26.4 and 45 s -1, which represent three shear rates within the stress plateau (low salt) or stress gradient (high salt) regions of the flow curves. Figure 8 displays the alignment and scattering patterns at an applied shear rate of γ = 45 s -1 for five positions across the gap taken with a narrow, straight slit (0.1 mm). The alignment factor for γ = 26.4 s -1 and γ = 15 s -1 are also shown at three gap positions. Additional measurements were taken on the 0.01% NaTos sample using a wider, 0.3 mm slit ( ) at the Institut Laue- Langevin, and a different configuration at NIST ( ) to demonstrate the versatility and reliability of the method. The alignment for the low salt sample (red) shows interesting features suggestive of shear banding that are absent in the high salt sample (blue). As seen in Figure 8 (left), at r/h 0.5 in the low salt solution, all of the alignment factors and respective scattering patterns appear identical for each shear rate. This alignment banding, evidenced by the constant alignment in the outer portion of the gap, is strongly suggestive of shear banding. In the low shear band, it is expected that the micelles are entangled and will align little within the band. The 2-D scattering patterns shown below the figure at γ = 45 s -1 also support the shear banding thesis, as these patterns do not change in the outer half of the gap. Consequently, the underlying intensity distribution which is used to calculate the alignment factor is identical in all three measurements. As the intensity distribution is a projection of the orientation distribution function of the material and changes based on the material microstructure, these measurements indicate that the same structure is present in the outer half of the gap. This alignment banding also implies the absence of shear thinning within the low shear band, which agrees with the PIV measurements of Helgeson et al. (2009b) that indicate little change in material structure across the low shear band for a related system. Conversely, the behavior of the high salt sample (blue) exhibits a gradual decrease in alignment as a function of gap position. A weak, continuous gradient in alignment is evident in the 2-D scattering patterns, where the sample becomes nearly isotropic close to the outer wall. This behavior is expected from a material that exhibits continuous shear thinning, as the decreasing shear rate with increasing gap position should correspond to a lower degree of segmental alignment with increasing gap position in such materials. The results also agree with visual observations from Helgeson et al. (2009a) comparing shear banding and non-shear banding solutions. In their work, there was a significant change in alignment and visual scattering from the inner to the outer wall in the shear banding CTAB sample, in accordance with the scattering from our low salt sample. However, the nonbanding CTAB sample showed little difference in the scattering across the gap, in agreement with the scattering from our high salt solution. The 1-3 alignment factor for each sample at each of the three shear rates is noted with the symbol in Figure 8. While often (incorrectly) assumed that the 1-3 alignment factor represents an average alignment across the gap, the 1-3 alignment factor here is clearly below the average for the 1-2 plane alignment. Any inference that could be made about the gap behavior from the 1-3 plane alignment factor would fail to identify differences between the two samples due to their similar 1-3 plane alignment trends. The 1-2 plane SANS data, however, show strong evidence to support the shear banding and shear thinning in the low and high salt WLM systems, respectively. 17

18 Figure 8: Alignment factor and 1-2 plane flow-sans scattering patterns at applied shear rates of 45, 26.4 and 15 s -1 of the low salt (0.01% wt NaTos) and high salt (0.10% wt NaTos) solutions. The symbols represent the primary set of experiments from the NIST Center for Neutron Research using a 0.1 mm fine slit, whereas the and symbols represent two sets of experiments using a 0.1 mm slit at NIST and a 0.3 mm curved slit at the Institut Laue-Langevin, respectively. The insets show the flow curve and the relative location of the three shear rates. The mechanism of shear banding is supported in the low salt system, as observed by a constant value of the alignment at r/h 0.5 at the three shear rates. Conversely, the 1-2 plane alignment provides evidence of shear thinning only in the high salt system, as the alignment continually decreases across the gap at the three shear rates. The equivalent 1-3 plane alignment factor is shown by the symbols. Dotted lines are for visual aid only. 18